How do you use the Change of Base Formula and a calculator to evaluate ${log}_{π} (\sqrt{2})$ $log_pi (sqrt{2})$ ?

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How do you use the Change of Base Formula and a calculator to evaluate ${log}_{π} (\sqrt{2})$ $log_pi (sqrt{2})$ ?

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Answer 1 · 2015-06-11T18:43:05

Take the log of the argument and divide by the log of the base.

${log}_{b} a = \frac{log a}{log b} = \frac{ln a}{ln b}$ $log_b a = log a / log b = ln a / ln b$

${log}_{π} \sqrt{2} = \frac{{ln 2}^{1/2}}{ln π} = \frac{\frac{1}{2} ln 2}{ln π} = \frac{ln 2}{2 ln π}$ $log_pi sqrt2 = ln2^("1/2") / (lnpi) = (1/2ln 2) / ln pi = ln2/(2lnpi)$

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How do you use the Change of Base Formula and a calculator to evaluate ${log}_{π} (\sqrt{2})$ $log_pi (sqrt{2})$ ?

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How do you use the Change of Base Formula and a calculator to evaluate ${log}_{π} (\sqrt{2})$ $log_pi (sqrt{2})$ ?